Vortex shedding as a precursor of turbulent electrical activity in cardiac muscle

Cabo, Cándido; Pertsov, Arkady M.; Davidenko, Jorge M.; Baxter, William T.; Gray, Richard A.; Jalife, José

doi:10.1016/s0006-3495(96)79691-1

Cited by 133 publications

(113 citation statements)

References 20 publications

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“…19) and to the catalytic CO oxidation on a platinum surface [207]. Cabo et al pointed out that such a vortex shedding at obstacles to propagation may be behind formation of spirals in cardiac tissue [145].…”

Section: Geometry Effectsmentioning

confidence: 99%

Nonlinear physics of electrical wave propagation in the heart: a review

2016

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Abstract. The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.

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Section: Geometry Effectsmentioning

confidence: 99%

Nonlinear physics of electrical wave propagation in the heart: a review

2016

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“…However, Cabo et al (10) found that spiral formation at an inexcitable barrier in sheep epicardial tissue occurred only if the interval between stimuli did not exceed Ͼ10% of the refractory period of the tissue. A similar condition has also been proposed theoretically by Pertsov et al (50).…”

Section: Discussionmentioning

confidence: 99%

“…They showed that when an electrical wave bends around an inexcitable strip, the wave detaches from the boundary with the formation of a tip; this tip eventually evolves into a rotating spiral wave. This effect was then studied theoretically and experimentally by Cabo et al (10) in sheep epicardial tissue, by using voltagesensitive dyes and video imaging techniques, under the influence of high-frequency stimulations or with partial blockage of the Na ϩ channels of the myocyte cell membrane. Such destabilization led to the formation of self-sustained vortices of electrical activity in the heart, in a manner similar to vortex shedding in hydrodynamic flows past obstacles (73).…”

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confidence: 99%

Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue

Majumder

Pandit

Panfilov

2014

American Journal of Physiology-Heart and Circulatory Physiology

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Majumder R, Pandit R, Panfilov AV. Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue. Am J Physiol Heart Circ Physiol 307: H1024 -H1035, 2014. First published August 8, 2014; doi:10.1152/ajpheart.00593.2013.-Wave propagation around various geometric expansions, structures, and obstacles in cardiac tissue may result in the formation of unidirectional block of wave propagation and the onset of reentrant arrhythmias in the heart. Therefore, we investigated the conditions under which reentrant spiral waves can be generated by high-frequency stimulation at sharp-edged obstacles in the ten TusscherNoble-Noble-Panfilov (TNNP) ionic model for human cardiac tissue. We show that, in a large range of parameters that account for the conductance of major inward and outward ionic currents of the model [fast inward Na ϩ current (INa), L-type slow inward Ca 2ϩ current (ICaL), slow delayed-rectifier current (IKs), rapid delayed-rectifier current (IKr), inward rectifier K ϩ current (IK1)], the critical period necessary for spiral formation is close to the period of a spiral wave rotating in the same tissue. We also show that there is a minimal size of the obstacle for which formation of spirals is possible; this size is ϳ2.5 cm and decreases with a decrease in the excitability of cardiac tissue. We show that other factors, such as the obstacle thickness and direction of wave propagation in relation to the obstacle, are of secondary importance and affect the conditions for spiral wave initiation only slightly. We also perform studies for obstacle shapes derived from experimental measurements of infarction scars and show that the formation of spiral waves there is facilitated by tissue remodeling around it. Overall, we demonstrate that the formation of reentrant sources around inexcitable obstacles is a potential mechanism for the onset of cardiac arrhythmias in the presence of a fast heart rate. cardiac arrhythmias; computer modeling; reentry; spiral waves; pacing

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“…[5]. The waves of excitation in cardiac tissue that initiate cardiac contraction are also being intensively studied, as abnormal wave propagation in the heart may lead to the formation of vortices and results in dangerous cardiac arrhythmias [6,7]. The key parameter that characterizes a propagating wave is its velocity; it turns out that the velocity of wave propagation in RD systems is affected by several factors, the curvature of the wave front being one of the most important.…”

mentioning

confidence: 99%

“…A highly important emergent phenomenon is wave propagation, which is found in many RD systems such as flame-front propagation [1], waves in the Belousov-Zhabotinsky reaction [2], chemotactic signaling during morphogenesis of a social amoeba [3], waves of intracellular calcium [4], and electrical signaling in neuronal tissue [5]. The waves of excitation in cardiac tissue that initiate cardiac contraction are also being intensively studied, as abnormal wave propagation in the heart may lead to the formation of vortices and results in dangerous cardiac arrhythmias [6,7]. The key parameter that characterizes a propagating wave is its velocity; it turns out that the velocity of wave propagation in RD systems is affected by several factors, the curvature of the wave front being one of the most important.…”

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confidence: 99%

Accurate Eikonal-Curvature Relation for Wave Fronts in Locally Anisotropic Reaction-Diffusion Systems

2011

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1The dependency of wave velocity in reaction-diffusion (RD) systems on the local front curvature determines not only the stability of wave propagation, but also the fundamental properties of other spatial configurations such as vortices. This Letter gives the first derivation of a covariant eikonal-curvature relation applicable to general RD systems with spatially varying anisotropic diffusion properties, such as cardiac tissue. The theoretical prediction that waves which seem planar can nevertheless possess a nonvanishing geometrical curvature induced by local anisotropy is confirmed by numerical simulations, which reveal deviations up to 20% from the nominal plane wave speed. [5]. The waves of excitation in cardiac tissue that initiate cardiac contraction are also being intensively studied, as abnormal wave propagation in the heart may lead to the formation of vortices and results in dangerous cardiac arrhythmias [6,7]. The key parameter that characterizes a propagating wave is its velocity; it turns out that the velocity of wave propagation in RD systems is affected by several factors, the curvature of the wave front being one of the most important. The dependency of the wave velocity on front curvature, i.e., the eikonal-curvature relation, was found in many systems [4,[8][9][10], and it was also shown to be essential to the stability of the wave front and properties of vortices in the particular RD system. The simplest eikonal-curvature relation is given by the following linear relationship [8,9]:with c 0 the speed of a traveling plane wave in the given medium and a medium-dependent constant close to the scalar diffusivity of the isotropic medium [8,11]. Although stability analysis of Eq. (1) ensures stable propagating waves for positive , stability in critical media where lies close to zero is not guaranteed [12]. Remarkably, even when > 0, the linearized equation (1) Fortunately, the mathematical treatment of local anisotropy is greatly simplified when the curved-space formalism introduced in [15] is adopted. This formalism will not only allow us to generalize Eq. (1) to homogeneous excitable media of an arbitrary anisotropy type, but it also simplifies calculations such that the quadratic curvature corrections to the wave speed can be calculated for the first time. Our mathematical derivation provides an alternative and a generalization to Keener's seminal proof for the isotropic case, which relies on a boundary layer approximation and is thus restricted to the limit of steep wave fronts [9]. Here, Kuramoto's approach [8] is elaborated in a Riemannian context and pursued to higher order in curvature.To start the derivation, the set of coupled reactiondiffusion equations (RDE) is written in terms of a column matrix u of state variables u ðmÞ , with the summation convention for repeated spatial indices, @ t uðr; tÞ ¼ @ i ðD ij ðrÞ@ j Puðr; tÞÞ þ Fðuðr; tÞÞ:Local anisotropy of the medium is embodied by the spatially varying diffusion tensor D ij ðrÞ. The constant projection matrix P selects only those sta...

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Vortex shedding as a precursor of turbulent electrical activity in cardiac muscle

Cited by 133 publications

References 20 publications

Nonlinear physics of electrical wave propagation in the heart: a review

Nonlinear physics of electrical wave propagation in the heart: a review

Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue

Accurate Eikonal-Curvature Relation for Wave Fronts in Locally Anisotropic Reaction-Diffusion Systems

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